Initial data commit

Task/Multiplicative-order/Julia/multiplicative-order.julia

@@ -0,0 +1,25 @@
+using Primes
+
+function factors(n)
+    f = [one(n)]
+    for (p,e) in factor(n)
+        f = reduce(vcat, [f*p^j for j in 1:e], init=f)
+    end
+    return length(f) == 1 ? [one(n), n] : sort!(f)
+end
+
+function multorder(a, m)
+    gcd(a,m) == 1 || error("$a and $m are not coprime")
+    res = one(m)
+    for (p,e) in factor(m)
+        m = p^e
+        t = div(m, p) * (p-1)
+        for f in factors(t)
+            if powermod(a, f, m) == 1
+                res = lcm(res, f)
+                break
+            end
+        end
+    end
+    res
+end